Final answer:
To find the inverse Laplace transform of F(s) = (s+3)/(s^2(s^2+15s+56)), use partial fraction decomposition to split the expression into simpler terms, find the values of A, B, C, and D, and then use the inverse Laplace transform formulas to find the final answer.
Step-by-step explanation:
To find the inverse Laplace transform of F(s) = (s+3)/(s^2(s^2+15s+56)), we can use partial fraction decomposition to split the expression into simpler terms. The denominator can be factored as (s+7)(s+8), so we can write F(s) as F(s) = A/s + B/s^2 + C/(s+7) + D/(s+8). After finding the values of A, B, C, and D, we can use the formulas for the inverse Laplace transform of each term to find the final answer.